2020 SAJC P2 Q7
2020 SAJC P2 Q7
8 marks
Prelims
A manufacturing company produces semi-conductor chips. On average, for every \(1000\) semi-conductor chips that were manufactured, \(p\) would be faulty. The semi-conductor chips are packaged in boxes of \(50\) before selling to end users.
- State, in context two assumptions needed for the number of faulty semi-conductor chips to be well modelled by binomial distribution.[2]
Assume now the assumptions in (i) do in fact hold.
- It is given that in a box of \(50\) semi-conductor chips, the probability that it contains at most \(1\) faulty semi-conductor chip is \(0.336\). Write down an equation for \(p\) and solve for this value numerically, correct to the nearest integer.[4]
- Using the value of \(p\) found in (ii), find the probability that among the two randomly selected boxes of semi-conductor chips, one box has at most \(3\) faulty semi-conductor chips and the other box has exactly \(5\) faulty semi-conductor chips.[2]
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Answer:(i)1) In the box of \({50}\) semi-conductor chips, the event that observing the condition of one semi-conductor(whether it is faulty or not) is independent of the event of observing the condition of any other semi-conductor chips. 2) The probability that a semi-conductor chip is faulty is constant at \({\frac{p}{1000}}\) for every semi-conductor \({0.336}\) chip. (ii) \({p=45}\) (nearest integer)
(iii) \({0.0801}\) (3 s.f.)
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